Mr. and Mrs. Samson are planning to build a fence around their garden, so they compare two different designs.
Design A:
Posts: 4 1/4 feet in length. Post must be installed 7/8 below ground level.
Design B: Posts: 6 3/4 feet in length.
Posts must be installed 1 1/2 feet below ground level.
1. What will be the height of the fence in design A?
2. What will be the height of the fence in design B?
3. Which fence will be taller and by how much?
(Complete each question step-by-step.)
To find the height of the fence in design A, we need to add the length of the posts to the height they are installed below ground level.
1. The length of the posts in design A is 4 1/4 feet.
2. The posts in design A are installed 7/8 feet below ground level.
To find the total height, we add the length of the posts and the depth they are installed below ground level:
4 1/4 feet + 7/8 feet = 4.25 feet + 0.875 feet = 5.125 feet
Therefore, the height of the fence in design A is 5.125 feet.
Now, let's find the height of the fence in design B using the same steps:
1. The length of the posts in design B is 6 3/4 feet.
2. The posts in design B are installed 1 1/2 feet below ground level.
To find the total height, we add the length of the posts and the depth they are installed below ground level:
6 3/4 feet + 1 1/2 feet = 6.75 feet + 1.5 feet = 8.25 feet
Therefore, the height of the fence in design B is 8.25 feet.
To determine which fence will be taller and by how much, we subtract the height of the fence in design A from the height of the fence in design B:
8.25 feet - 5.125 feet = 3.125 feet
Therefore, the fence in design B will be taller than the fence in design A by 3.125 feet.
Step 1: Convert all measurements to the same unit of measurement. Let's convert the measurements to inches for easier comparison.
Design A:
Posts: 4 1/4 feet in length.
To convert feet to inches, multiply by 12.
4 1/4 feet = (4 * 12) + 1/4 = 48 + 3 = 51 inches.
Design B:
Posts: 6 3/4 feet in length.
6 3/4 feet = (6 * 12) + 3/4 = 72 + 9 = 81 inches.
Step 2: Determine the height of the fence for each design.
Design A:
The posts need to be installed 7/8 below ground level.
To find the height above ground level, subtract the portion below ground from the total length of the posts.
Height of fence in design A = 51 inches - (7/8 * 12 inches) = 51 inches - 10.5 inches = 40.5 inches.
Design B:
The posts need to be installed 1 1/2 feet below ground level.
To find the height above ground level, subtract the portion below ground from the total length of the posts.
Height of fence in design B = 81 inches - (1 1/2 * 12 inches) = 81 inches - 18 inches = 63 inches.
Step 3: Compare the heights of the fences to determine which one is taller and by how much.
Comparing design A (40.5 inches) and design B (63 inches):
Design B is taller than design A by 63 inches - 40.5 inches = 22.5 inches.
Therefore:
1. The height of the fence in design A is 40.5 inches.
2. The height of the fence in design B is 63 inches.
3. The fence in design B is taller than the fence in design A by 22.5 inches.